Answer
(a) $t=\frac{\ln\frac{10}{3}}{12\ln\frac{41}{40}}$
(b) $t\approx 4.063202$
Work Step by Step
(a) We need to solve:
$300(1.025)^{12t}=1000$
$(1.025)^{12t}=\frac{1000}{300}$
$(\frac{41}{40})^{12t}=\frac{10}{3}$
We take the natural log of both sides and use log rules to simplify:
$12t\ln\frac{41}{40}=\ln\frac{10}{3}$
$12t=\frac{\ln\frac{10}{3}}{\ln\frac{41}{40}}$
$t=\frac{\ln\frac{10}{3}}{12\ln\frac{41}{40}}$
(b) We solve using a calculator:
$t\approx 4.063202$
